Cavity quantum electrodynamics (CQED) offers promising approaches for implementing quantum information processing. Quantum networks combine the ease of storing and manipulating quantum information in atoms, ions, or quantum dots, with the advantages of transferring information between nodes via photons, using coherent interfaces. So far, demonstrations of basic building blocks of such networks have relied on atomic systems. Successful solid-state implementation of these building blocks would open new opportunities leading to practical quantum information processing systems.
Semiconductor CQED has enjoyed recent rapid progress largely due to the development of high quality factor optical micro-cavities with mode volumes less than a cubic wavelength of light. These cavities allow previously unattainable interaction strengths between a cavity mode and a dipole emitter such as a quantum dot. Examples of applications requiring strong interactions between a cavity and dipole include methods for imparting conditional phase shifts on single photons, atom number detection, and non-linear optics.
One property of a cavity-dipole interaction is that, under appropriate conditions, the dipole can switch the cavity from being highly transmissive to being highly reflective. This can result in entanglement between the dipole and reflected field.
It has long been believed that in order for a dipole to fully switch a cavity, the vacuum Rabi frequency of the dipole must exceed both the cavity and dipole decay rates. Although this strong coupling regime has been attained in atomic systems, it is difficult to achieve using semiconductor technology. Semiconductor implementations of cavity QED systems, such as photonic crystal cavities coupled to quantum dots, usually suffer from large out-of-plane losses, resulting in short cavity lifetimes. Things become even more difficult when one attempts to integrate cavities with waveguides. The cavity-waveguide coupling rate must be sufficiently large that not too much field is lost out-of-plane. At the same time, leakage into the waveguide introduces additional losses, making the strong coupling regime even more difficult to achieve.
Systems and methods are needed that remove the necessity of using the strong coupling regime, allowing complete switching in a more practical parameter regime for semiconductors.
One of the main limitations of quantum communication is that communication rates decay exponentially with distance due to large losses induced by optical channels. In classical communication, channel losses can be overcome by optical amplifiers placed along the path of a fiber. At each amplifier node, the signal is boosted to overcome the fiber losses. This solution is not possible in quantum communication because amplification injects quantum noise into the channel, which destroys the state of the qubit.
The exchange of quantum bits over long distances can be achieved by creating an entangled state between two communication points. Quantum teleportation can be used to exchange qubits between nodes. Entanglement can be generated over long distance by creating entanglement between a large number of intermediate nodes (or repeater stations), which are spaced by short distances along the communication path. Entanglement swapping can then be used to create entanglement between the two end nodes. This procedure can be made fault tolerant by using entanglement purification protocols.
Quantum repeaters can be implemented in a variety of systems. All optical proposals, as well as proposals based on atomic systems have been extensively studied. More recent proposals rely on optically controlled spins in semiconductor cavities interacting with coherent light.
Systems and methods are needed for implementing quantum repeaters by exploiting cavity-dipole interactions in semiconductor systems.
Symbols used to denote various quantities in CQED have varied in the literature, including in our own work. Table 1 provides definitions for symbols used herein:
TABLE 1Definitions of various symbols.SymbolDefinition2gRabi frequency; dipole - electric field couplingstrengthγDipole decay rate into modes other than the cavitymode and to non-radiative decay routes;approximately equal to the bare dipole decay rateκ = ω0/2QCavity field decay rateω0Cavity resonant frequencyQCavity quality factorηEnergy decay rate from a cavity into eachwaveguide in a coupled cavity - waveguide system